Elements of the Conic Sections |
Common terms and phrases
abfurd alfo alſo baſe becauſe bifected bola cafe centre confequently conjugate diameters conjugate hyperbolas defcribed diame diameter conjugated directrix diſtance draw drawn parallel Elem equal excefs fecond axis fecond diameter fection fegments femidiameter fince foci focus fquare of CB ftraight line drawn ftraight line parallel furface given in pofition greater axis interfect join latus rectum lefs let it meet likewife line be drawn meeting the afymptotes meets the hyperbola meter oppofite hyperbolas paffes paffing perbola perpendicular plane point D point G point of contact poſition PROP propofition rallel rect rectangle AMB rectangle contained right angles ſquare ſtraight line ordinately ſtraight line touching tangent THEOR ther theſe touch the parabola touches the ellipfe touches the hyperbola tranfverfe axis tranfverfe diameter tranſverſe triangle vertex vertices
Popular passages
Page 51 - Fig. is. of which is A, BC being the circle in the circumference of which the straight line revolves which describes the surface; let it be cut by any plane parallel to the circle BC, and let this plane make in it a section DLE : The line DLE is the circumference of a circle the centre of which is in the axis. Take the centre of the circle BC, and let it be F; join AF ; AF, consequently, is (def. 10.) the axis, and meets the cutting plane ; let it meet it in G ; next, let any plane pass through the...
Page 54 - Elem.) base of the cone ; and, for this reason, the section DHE is (23. I.) a circle, of which DE is a diameter: the rectangle, therefore, contained by DF, FE is (35. 3. Elem.) equal to the square of FH. And since ED is parallel to BC, the angle ADE is equal to the angle ABC ; and the angle AKG is placed equal to the angle ABC; therefore the angle AKG is also equal to ADE : and the angles at F are equal, for they are opposite vertical angles ; therefore the triangle DFG is similar to the triangle...
Page 48 - ... point without the plane of it, be moved around the circumference without ceasing to pass through the point, the surface generated is called a conic surface, and the solid terminated by the surface is called a cone. II. The point is called the vertex, and the circle the base of the cone. The straight line drawn from the vertex to the centre of the circle, is called the axis. If the axis be perpendicular to the plane of the base, the cone is said to be right. III. If the generating line be produced...
Page 249 - A and base the circle BF, and let it be cut by a plane through the axis, and let the section so made be the...
Page 2 - If from a point of the parabola, D, (fig. 2) a right line be drawn to the focus, C ; and another, DA, perpendicular to the directrix ; then shall the right line, DE, which bisects the angle, ADC, contained between...
Page 202 - If a tangent to an ellipse meet a diameter, and from the point of contact an ordinate be drawn to that diameter ; the semidiameter will be a mean proportional between the segments of the diameter intercepted between the centre and the ordinate, and between the centre and the tangent. Let DH, a tangent to the ellipse at D, meet the diameter PJO produced in H, and let I)E«?
Page 115 - The fum of the fquares of' any two conjugate diameters is equal to the fum of the fquares of the two axes.